{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://raw.githubusercontent.com/Qiskit/qiskit-tutorials/master/images/qiskit-heading.png\" width=\"500 px\" align=\"center\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Grover Search for Combinatorial Problems\n",
    "\n",
    "This notebook is based on an official notebook by Qiskit team, available at https://github.com/qiskit/qiskit-tutorial under the [Apache License 2.0](https://github.com/Qiskit/qiskit-tutorial/blob/master/LICENSE) license. \n",
    "Initially done by Giacomo Nannicini and Rudy Raymond (based on [this paper](https://arxiv.org/abs/1708.03684)).\n",
    "\n",
    "Your **TASK** is to follow the tutorial, as you implement the Grover algorithm (studied this week) to a real SAT problem!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "Grover search is one of the most popular algorithms used for searching a solution among many possible candidates using Quantum Computers. If there are $N$ possible solutions among which there is exactly one solution (that can be verified by some function evaluation), then Grover search can be used to find the solution with $O(\\sqrt{N})$ function evaluations. This is in contrast to classical computers that require $\\Omega(N)$ function evaluations: the Grover search is a quantum algorithm that provably can be used search the correct solutions quadratically faster than its classical counterparts.  \n",
    "\n",
    "Here, we are going to illustrate the use of Grover search to solve a combinatorial problem called [Exactly-1 3-SAT problem](https://en.wikipedia.org/wiki/Boolean_satisfiability_problem#Exactly-1_3-satisfiability). The Exactly-1 3-SAT problem is a NP-complete problem, namely, it is one of the most difficult problems that are interconnected (meaning that if we solve any one of them, we essentially can solve all of them). Unfortunately, there are many natural problems that are NP-complete, such as, the Traveling Salesman Problem (TSP), the Maximum Cut (MaxCut) and so on. Up to now, there is no classical and quantum algorithm that can efficiently solve such NP-hard problems. \n",
    "\n",
    "We begin with an example of the Exactly-1 3-SAT problem. Then, we show how to design an evaluation function which is also known as the oracle (or, blackbox) which is essential to Grover search. Finally, we show the circuit of Grover search using the oracle and present their results on simulator and real-device backends."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exactly-1 3-SAT problem\n",
    "\n",
    "The Exactly-1 3-SAT problem is best explained with the following concrete problem. Let us consider a Boolean function $f$ with three Boolean variables $x_1, x_2, x_3$ as below.\n",
    "\n",
    "$$\n",
    "f(x_1, x_2, x_3) = (x_1 \\vee x_2 \\vee \\neg x_3) \\wedge (\\neg x_1 \\vee \\neg x_2 \\vee \\neg x_3) \\wedge (\\neg x_1 \\vee x_2 \\vee x_3) \n",
    "$$\n",
    "\n",
    "In the above function, the terms on the right-hand side equation which are inside $()$ are called clauses. Each clause has exactly three literals. Namely, the first clause has $x_1$, $x_2$ and $\\neg x_3$ as its literals. The symbol $\\neg$ is the Boolean NOT that negates (or, flips) the value of its succeeding literal. The symbols $\\vee$ and $\\wedge$ are, respectively, the Boolean OR and AND. The Boolean $f$ is satisfiable if there is an assignment of $x_1, x_2, x_3$ that evaluates to $f(x_1, x_2, x_3) = 1$ (or, $f$ evaluates to True). The Exactly-1 3-SAT problem requires us to find an assignment such that $f = 1$ (or, True) and there is *exactly* one literal that evaluates to True in every clause of $f$. \n",
    "\n",
    "A naive way to find such an assignment is by trying every possible combinations of input values of $f$. Below is the table obtained from trying all possible combinations of $x_1, x_2, x_3$. For ease of explanation, we interchangably use $0$ and False, as well as $1$ and True.  \n",
    "\n",
    "|$x_1$ | $x_2$ | $x_3$ | $f$ | Comment | \n",
    "|------|-------|-------|-----|---------|\n",
    "| 0    |  0    |  0    |  1  | Not a solution because there are three True literals in the second clause     | \n",
    "| 0    |  0    |  1    |  0  | Not a solution because $f$ is False          | \n",
    "| 0    |  1    |  0    |  1  | Not a solution because there are two True literals in the first clause        | \n",
    "| 0    |  1    |  1    |  1  | Not a solution because there are three True literals in the third clause        | \n",
    "| 1    |  0    |  0    |  0  | Not a solution because $f$ is False        | \n",
    "| 1    |  0    |  1    |  1  | **Solution**. BINGO!!       | \n",
    "| 1    |  1    |  0    |  1  | Not a soluton because there are three True literals in the first clause        | \n",
    "| 1    |  1    |  1    |  0  | Not a solution because $f$ is False        | \n",
    "\n",
    "\n",
    "From the table above, we can see that the assignment $x_1x_2x_3 = 101$ is the solution fo the Exactly-1 3-SAT problem to $f$. In general, the Boolean function $f$ can have many clauses and more Boolean variables. \n",
    "\n",
    "## A blackbox function to check the assignment of Exactly-1 3-SAT problem\n",
    "\n",
    "Here, we describe a method to construct a circuit to check the assignment of Exactly-1 3-SAT problem. The circuit can then be used as a blackbox (or, oracle) in Grover search. To design the blackbox, we do not need to know the solution to the problem in advance: it suffices to design a blackbox that checks if the assignment results in $f$ evaluates to True or False. It turns out that we can design such a blackbox efficiently (in fact, any NP-complete problem has the property that although finding the solution is difficult, checking the solution is easy). \n",
    "\n",
    "For each clause of $f$, we design a sub-circuit that outputs True if and only if there is exactly one True literal in the clause. Combining all sub-circuits for all clauses, we can then obtain the blackbox that outputs True if and only if all clauses are satisfied with exactly one True literal each.   \n",
    "\n",
    "For example, let us consider the clause $(x_1 \\vee \\neg x_2 \\vee x_3)$. It is easy to see that $y$ defined as \n",
    "\n",
    "$$\n",
    "y = x_1 \\oplus \\neg x_2 \\oplus x_3 \\oplus ( x_1 \\wedge \\neg x_2 \\wedge x_3), \n",
    "$$\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as npis True if and only if exactly one of $x_1$, $\\neg x_2$, and $x_3$ is True. Using two working qubits, $y$ can be computed by the following sub-circuit. Below, $x_1x_2x_3$ is renamed as $q_1q_2q_3$, $q_4$ is used as a working qubit, and $q_5$ is used to store the value of $y$.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T17:34:42.934376Z",
     "start_time": "2018-09-25T17:34:42.923743Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "# importing Qiskit\n",
    "from qiskit import Aer, IBMQ\n",
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister\n",
    "from qiskit import available_backends, execute, register, get_backend, compile\n",
    "\n",
    "from qiskit.tools import visualization\n",
    "from qiskit.tools.visualization import circuit_drawer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T17:32:05.667148Z",
     "start_time": "2018-09-25T17:32:03.983610Z"
    }
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=569x264 at 0x1CAAF817048>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = QuantumRegister(6)\n",
    "qc = QuantumCircuit(q)\n",
    "qc.x(q[2])\n",
    "qc.cx(q[1], q[5])\n",
    "qc.cx(q[2], q[5])\n",
    "qc.cx(q[3], q[5])\n",
    "qc.ccx(q[1], q[2], q[4])\n",
    "qc.ccx(q[3], q[4], q[5])\n",
    "qc.ccx(q[1], q[2], q[4])\n",
    "qc.x(q[2])\n",
    "circuit_drawer(qc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the sub-circuit above, the three `ccx` gates on the right are used to compute $( q_1 \\wedge \\neg q_2 \\wedge q_3)$ and write the result to $q_5$, while the three `cx` gates on the left are used to compute $q_1 \\oplus \\neg q_2 \\oplus q_3$ and write the result to $q_5$. Notice that the right-most `ccx` gate is used to reset the value of $q_4$ so that it can be reused in the succeeding sub-circuits. \n",
    "\n",
    "From the above sub-circuit, we can define a blackbox function to check the solution of the Exactly-1 3-SAT problem as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T17:32:05.678916Z",
     "start_time": "2018-09-25T17:32:05.669852Z"
    }
   },
   "outputs": [],
   "source": [
    "def black_box_u_f(circuit, f_in, f_out, aux, n, exactly_1_3_sat_formula):\n",
    "    \"\"\"Circuit that computes the black-box function from f_in to f_out.\n",
    "\n",
    "    Create a circuit that verifies whether a given exactly-1 3-SAT\n",
    "    formula is satisfied by the input. The exactly-1 version\n",
    "    requires exactly one literal out of every clause to be satisfied.\n",
    "    \"\"\"\n",
    "    num_clauses = len(exactly_1_3_sat_formula)\n",
    "    for (k, clause) in enumerate(exactly_1_3_sat_formula):\n",
    "        # This loop ensures aux[k] is 1 if an odd number of literals\n",
    "        # are true\n",
    "        for literal in clause:\n",
    "            if literal > 0:\n",
    "                circuit.cx(f_in[literal-1], aux[k])\n",
    "            else:\n",
    "                circuit.x(f_in[-literal-1])\n",
    "                circuit.cx(f_in[-literal-1], aux[k])\n",
    "        # Flip aux[k] if all literals are true, using auxiliary qubit\n",
    "        # (ancilla) aux[num_clauses]\n",
    "        circuit.ccx(f_in[0], f_in[1], aux[num_clauses])\n",
    "        circuit.ccx(f_in[2], aux[num_clauses], aux[k])\n",
    "        # Flip back to reverse state of negative literals and ancilla\n",
    "        circuit.ccx(f_in[0], f_in[1], aux[num_clauses])\n",
    "        for literal in clause:\n",
    "            if literal < 0:\n",
    "                circuit.x(f_in[-literal-1])\n",
    "    # The formula is satisfied if and only if all auxiliary qubits\n",
    "    # except aux[num_clauses] are 1\n",
    "    if (num_clauses == 1):\n",
    "        circuit.cx(aux[0], f_out[0])\n",
    "    elif (num_clauses == 2):\n",
    "        circuit.ccx(aux[0], aux[1], f_out[0])\n",
    "    elif (num_clauses == 3):\n",
    "        circuit.ccx(aux[0], aux[1], aux[num_clauses])\n",
    "        circuit.ccx(aux[2], aux[num_clauses], f_out[0])\n",
    "        circuit.ccx(aux[0], aux[1], aux[num_clauses])\n",
    "    else:\n",
    "        raise ValueError('We only allow at most 3 clauses')\n",
    "    # Flip back any auxiliary qubits to make sure state is consistent\n",
    "    # for future executions of this routine; same loop as above.\n",
    "    for (k, clause) in enumerate(exactly_1_3_sat_formula):\n",
    "        for literal in clause:\n",
    "            if literal > 0:\n",
    "                circuit.cx(f_in[literal-1], aux[k])\n",
    "            else:\n",
    "                circuit.x(f_in[-literal-1])\n",
    "                circuit.cx(f_in[-literal-1], aux[k])\n",
    "        circuit.ccx(f_in[0], f_in[1], aux[num_clauses])\n",
    "        circuit.ccx(f_in[2], aux[num_clauses], aux[k])\n",
    "        circuit.ccx(f_in[0], f_in[1], aux[num_clauses])\n",
    "        for literal in clause:\n",
    "            if literal < 0:\n",
    "                circuit.x(f_in[-literal-1])\n",
    "# -- end function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inversion about the mean\n",
    "\n",
    "Another important procedure in Grover search is to have an operation that perfom the *inversion-about-the-mean* step, namely, it performs the following transformation:\n",
    "\n",
    "$$\n",
    "\\sum_{j=0}^{2^{n}-1} \\alpha_j |j\\rangle \\rightarrow \\sum_{j=0}^{2^{n}-1}\\left(2 \\left( \\sum_{k=0}^{k=2^{n}-1} \\frac{\\alpha_k}{2^n} \\right) - \\alpha_j  \\right) |j\\rangle \n",
    "$$\n",
    "\n",
    "The above transformation can be used to amplify the probability amplitude $\\alpha_s$ when s is the solution and $\\alpha_s$ is negative (and small), while $\\alpha_j$ for $j \\neq s$ is positive. Roughly speaking, the value of $\\alpha_s$ increases by twice the mean of the amplitudes, while others are reduced. The inversion-about-the-mean can be realized with the sequence of unitary matrices as below:\n",
    "\n",
    "$$\n",
    "H^{\\otimes n} \\left(2|0\\rangle \\langle 0 | - I \\right) H^{\\otimes n}\n",
    "$$\n",
    "\n",
    "The first and last $H$ are just Hadamard gates applied to each qubit. The operation in the middle requires us to design a sub-circuit that flips the probability amplitude of the component of the quantum state corresponding to the all-zero binary string. The sub-circuit can be realized by the following function, which is a multi-qubit controlled-Z which flips the probability amplitude of the component of the quantum state corresponding to the all-one binary string. Applying X gates to all qubits before and after the function realizes the sub-circuit. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T17:32:08.246809Z",
     "start_time": "2018-09-25T17:32:08.236159Z"
    }
   },
   "outputs": [],
   "source": [
    "def n_controlled_Z(circuit, controls, target):\n",
    "    \"\"\"Implement a Z gate with multiple controls\"\"\"\n",
    "    if (len(controls) > 2):\n",
    "        raise ValueError('The controlled Z with more than 2 ' +\n",
    "                         'controls is not implemented')\n",
    "    elif (len(controls) == 1):\n",
    "        circuit.h(target)\n",
    "        circuit.cx(controls[0], target)\n",
    "        circuit.h(target)\n",
    "    elif (len(controls) == 2):\n",
    "        circuit.h(target)\n",
    "        circuit.ccx(controls[0], controls[1], target)\n",
    "        circuit.h(target)\n",
    "# -- end function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, the inversion-about-the-mean circuit can be realized by the following function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T17:32:09.200728Z",
     "start_time": "2018-09-25T17:32:09.196905Z"
    }
   },
   "outputs": [],
   "source": [
    "def inversion_about_mean(circuit, f_in, n):\n",
    "    \"\"\"Apply inversion about the mean step of Grover's algorithm.\"\"\"\n",
    "    # Hadamards everywhere\n",
    "    for j in range(n):\n",
    "        circuit.h(f_in[j])\n",
    "    # D matrix: flips the sign of the state |000> only\n",
    "    for j in range(n):\n",
    "        circuit.x(f_in[j])\n",
    "    n_controlled_Z(circuit, [f_in[j] for j in range(n-1)], f_in[n-1])\n",
    "    for j in range(n):\n",
    "        circuit.x(f_in[j])\n",
    "    # Hadamards everywhere again\n",
    "    for j in range(n):\n",
    "        circuit.h(f_in[j])\n",
    "# -- end function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a circuit of the inversion about the mean on three qubits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T17:32:11.403205Z",
     "start_time": "2018-09-25T17:32:10.138028Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=862x138 at 0x1CA9C4719B0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qr = QuantumRegister(3)\n",
    "qInvAvg = QuantumCircuit(qr)\n",
    "inversion_about_mean(qInvAvg, qr, 3)\n",
    "circuit_drawer(qInvAvg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Grover Search: putting all together\n",
    "\n",
    "The complete steps of Grover search is as follow.\n",
    "\n",
    "1. Create the superposition of all possible solutions as the initial state (with working qubits initialized to zero)\n",
    "$$  \\sum_{j=0}^{2^{n}-1} \\frac{1}{2^n} |j\\rangle |0\\rangle$$\n",
    "2. Repeat for $T$ times:\n",
    "\n",
    "     * Apply the `blackbox` function\n",
    "    \n",
    "     * Apply the `inversion-about-the-mean` function\n",
    "    \n",
    "3. Measure to obtain the solution\n",
    "\n",
    "The code for the above steps is as below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T17:37:05.873175Z",
     "start_time": "2018-09-25T17:34:42.936448Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1caaf86c908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Grover search implemented in Qiskit.\n",
    "\n",
    "This module contains the code necessary to run Grover search on 3\n",
    "qubits, both with a simulator and with a real quantum computing\n",
    "device. This code is the companion for the paper\n",
    "\"An introduction to quantum computing, without the physics\",\n",
    "Giacomo Nannicini, https://arxiv.org/abs/1708.03684. \n",
    "\"\"\"\n",
    "\n",
    "def input_state(circuit, f_in, f_out, n):\n",
    "    \"\"\"(n+1)-qubit input state for Grover search.\"\"\"\n",
    "    for j in range(n):\n",
    "        circuit.h(f_in[j])\n",
    "    circuit.x(f_out)\n",
    "    circuit.h(f_out)\n",
    "# -- end function\n",
    "\n",
    "# Make a quantum program for the n-bit Grover search.\n",
    "n = 3\n",
    "\n",
    "# Exactly-1 3-SAT formula to be satisfied, in conjunctive\n",
    "# normal form. We represent literals with integers, positive or\n",
    "# negative, to indicate a Boolean variable or its negation.\n",
    "exactly_1_3_sat_formula = [[1, 2, -3], [-1, -2, -3], [-1, 2, 3]]\n",
    "\n",
    "# Define three quantum registers: 'f_in' is the search space (input\n",
    "# to the function f), 'f_out' is bit used for the output of function\n",
    "# f, aux are the auxiliary bits used by f to perform its\n",
    "# computation.\n",
    "f_in = QuantumRegister(n)\n",
    "f_out = QuantumRegister(1)\n",
    "aux = QuantumRegister(len(exactly_1_3_sat_formula) + 1)\n",
    "\n",
    "# Define classical register for algorithm result\n",
    "ans = ClassicalRegister(n)\n",
    "\n",
    "# Define quantum circuit with above registers\n",
    "grover = QuantumCircuit()\n",
    "grover.add(f_in)\n",
    "grover.add(f_out)\n",
    "grover.add(aux)\n",
    "grover.add(ans)\n",
    "\n",
    "input_state(grover, f_in, f_out, n)\n",
    "T = 2\n",
    "for t in range(T):\n",
    "    # Apply T full iterations\n",
    "    black_box_u_f(grover, f_in, f_out, aux, n, exactly_1_3_sat_formula)\n",
    "    inversion_about_mean(grover, f_in, n)\n",
    "\n",
    "# Measure the output register in the computational basis\n",
    "for j in range(n):\n",
    "    grover.measure(f_in[j], ans[j])\n",
    "\n",
    "# Execute circuit\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "job = execute([grover], backend=backend, shots=1000)\n",
    "result = job.result()\n",
    "\n",
    "# Get counts and plot histogram\n",
    "counts = result.get_counts(grover)\n",
    "visualization.plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Running the circuit in real devices\n",
    "\n",
    "We have seen that the simulator can find the solution to the combinatorial problem. We would like to see what happens if we use the real quantum devices that have noise and imperfect gates. \n",
    "\n",
    "However, due to the restriction on the length of strings that can be sent over the network to the real devices (there are more than sixty thousands charactes of QASM of the circuit), at the moment the above circuit cannot be run on real-device backends. We can see the compiled QASM on real-device `ibmqx5` backend as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "IBMQ.load_accounts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T18:41:39.542516Z",
     "start_time": "2018-09-25T18:41:28.052236Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of gates for ibmq_16_melbourne is 1982\n"
     ]
    }
   ],
   "source": [
    "# get ibmq_16_rueschlikon configuration and coupling map\n",
    "backend = IBMQ.get_backend('ibmq_16_melbourne')\n",
    "backend_config = backend.configuration()\n",
    "backend_coupling = backend_config['coupling_map']\n",
    "\n",
    "# compile the circuit for ibmq_16_rueschlikon\n",
    "grover_compiled = compile(grover, backend=backend, coupling_map=backend_coupling, seed=1)\n",
    "\n",
    "grover_compiled_qasm = grover_compiled.experiments[0].header.compiled_circuit_qasm\n",
    "print(\"Number of gates for\", backend.name(), \"is\", len(grover_compiled_qasm.split(\"\\n\")) - 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The number of gates is in the order of thousands which is above the limits of decoherence time of the current near-term quantum computers. It is a challenge to design a quantum circuit for Grover search to solve large optimization problems. \n",
    "\n",
    "### Free flow\n",
    "\n",
    "In addition to using too many gates, the circuit in this notebook uses auxiliary qubits. It is left as future work to improve the efficiency of the circuit as to make it possible to run it in the real devices. Below is the original circuit. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T18:42:03.016728Z",
     "start_time": "2018-09-25T18:41:52.288291Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fjBkzXBQfAAghTFGsTLAJAFCmULcBwDWotwAMwQTFygSbAACAPUxwyjP6ozImOARQhTkywej9EQAAGII5Bk4ATM8ExcoEmwAAZQ2lGwBcg3oLwBBMUKxMsAkAANySOc53hn5mzByHACiOiTPc0JVHXX/++efy5ctfe+21ChUq6B0LgNJyfh7nZ599tkmTJj169Ch6ve7uDRo0EEKkp6efPn3a6XdxpZMnTyrnrUaNGhW5gPL3uLi4K1eu3PRP5cuX79Wr16JFi6xWq9Zxwkz27NljsViEEI0aNfLx8Sl5YXMPLwBAU4MGDYqKihJCZGdnT506tchl3n777blz5wohOnfuvGTJEjc3N5eGCACmKFYm2AQAKFOo2wDgGtRbAIZggmJlgk0AAMAeRj/lmeBRGaMfAqjFBJlggv4IAAAMwQQDJwBlgQmKlQk2AQDKGko3ALgG9RaAIZigWJlgEwAAuCUTnO+M/syYCQ4BUAKzZrjRK4+KxowZc/vtt48YMULvQACowPl5nH18fDZu3BgeHl7cAmFhYcqLixcvOv0urrRv3z7lRXHzONeuXVt5sX///sL/GhMTc/bs2V9//VWb6GBOu3btUl7YM2LIX7hly5YaxmQHq9XKlOUKdgVQJAm7hoeHx4QJE5TXc+fOLfyTDIsXL37jjTeEEI0bN/7666+9vb1dHWIhEu5GHbE3oAUJ88qIxeomRtwECTNBR+wNaIG8kpkR67Ygqf6NvQEUJmG/oN6aAHsDqpMwqQxarAoy6CZImAx6YVcApkTX1oJBT3n5DPqoTEFGPAR0Ri0YMRNuYtD+SD7nY1cAAIok4QnCoAMnCfekjtgbUJ2ESWXQYlWQQTdBwmTQEXsDqiOpJEfpNjp2BVAkCbuGEeuthLtRR+wNaEHCvDJisbqJETdBwkzQEXsDMB/6tRaMeL67iUGfGctn0ENAf4SdDJrht2T0yqOWb7755tdff508efItJ7MGYAg3z+Nss9l+/PHHwYMHt2zZ8t5773311VcTExOFEGPGjKlbt279+vWzs7PzF86fqblIhw8fVl5Ur15d5aiF+PTTT8eOHTt27NirV6+qtc5r164pL2rWrFnkAvl/P3XqVOF/vf/++6tWrbpw4UK14kFZYP8vP5w8eVIZVFWqVEmLPmWPixcvjhs3rk6dOj4+Pt7e3rVq1Ro9evSFCxd0CUZf7AqgSJJ3jQEDBtSrV08IkZGRMWPGjIL/tHHjxmHDhgkhIiMjf/jhh+DgYH1CFEJIvxtdjL0BLUieV0YpViUwyiZIngkuxt6AFsgrozBK3RYk1b+xN4DCJO8X1FuDYm9AdZInlYGKVXEMtAmSJ4MrsSsAU6Jra81Ap7zCjPWoTHGMcgjojFozSiYUx1j9kXzOx64AABRJ8hOEgQZOku9JF2NvQHWSJ5WBilVxDLQJkieDi7E3oDqSykAo3UbErgCKJHnXMEq9lXw3uhh7A1qQPK+MUqxKYJRNkDwTXIy9AZgP/VprRjnfFcdYz4wVyUCHgP4IJxgow+1ngspTehaL5bXXXmvZsmW/fv30jgWASmwFnD9/vlOnTjctEBIS8ttvv9WuXVsI0aBBA5t9MjIylHn6a9WqZWcTh+THeeLECUfbdu/evVOnToX//sEHHyjr/Ouvv4psuH37dmWB6dOnF7nAq6++6uvrm5yc7GhIMIHBgwc3btzY0Vb5A4Vjx46VvOQXX3yhLNmjR49brjYuLk4I8e233zoaTwlWrFgREBBQuIb4+fktWbJExTeSH7sCKJLLuoaHh8f777/vXNuVK1fmD29SUlKUP+7ZsycwMFAIERYWdvz4cYdWePz4cSHE2rVrnYunMCpMQewNaME1eZWbmyuE+PDDD51rrnqxOnjwoBBiw4YNmjYpSPVNWL16tRDi9OnTzsVTGBWmIPYGtEBeud7MmTOFEBaLxYm2qtdtm832zDPP1KxZ04lgikNSFcTeAApzWb8YOnRo/fr1nWurRb1t3779ww8/7Fw8RaLCFMTegOpcllSDBg1q0qSJc221KFYtWrQYMGCA1k3yabEJQUFBb775pnPxFIkKk49dAZgSXdtOy5YtE0IkJiY611z1U96ECRNCQkK0bmLT7FEZJ+7OmOCGTsnojPabPn26EMJqtTrRVovx51NPPVW7dm2tm9g064/nzp0TQqxYscLReEpAPudjVwAAiuSyE8SUKVM8PT2da6vFwGnIkCHR0dHOxVMkTrUFsTegOpcl1cSJEwMCApxrq0WxGjhwYLNmzRxq8vjjjzdt2tTRN1JosQnNmzd/7LHHnIunSFSYgtgbUB1JpYvw8PCXXnrJubaql+7k5GQhxPz5852Lp0jkVT52BVAk13SNpKQkIcTSpUuda656vd28ebMQIjY21rl4CqPCFMTegBZck1dnz54VQqxcudK55qoXq59++kkIsX//fk2bFKT6JsyePVsIkZ2d7Vw8hVFhCmJvAOZDv7ZfgwYNYmJinGurxaV4Ly+v9957z6Em3t7ekydPdvSNNHpmzIm7Mya4oVMy+mMZ16lTp549ezrXVosMj4iIGDt2rHPx5Nu2bZsQYvv27Y421Kjy3HvvvQ8++KBDkTjRRC2zZs0SQmzdutWJtuPGjatcubLqIQEoJff8s3t8fHyLFi02bdokhPD393/sscfefvvtYcOGpaWl9e7dW5mmsGXLloWHBUWaM2dOTk6OEGLEiBF2NtFdSkqK8kKZgbowLy8v5cWNGzeKXCAmJiYrK2v58uUaRAcTunTp0unTp4UQoaGhUVFRJS+c/4MS9ndDFa1cubJ///7p6emF/ykzM3Pw4MFLlixxfVS6YFcARTJK13jkkUcaNWokhLh+/fpHH30khDh9+nS3bt3S0tICAgK+//77W1ZjTRllN7oGewNaMEpeSV6s7CH5JhglE1yDvQEtkFeGI3ndFiTVv7E3gMKM0i+ot8bC3oDqjJJU8herW5J/E4ySDC7ArgBMia7tMvKf8opkoEdlbknyQ0BndBnJM6EEBuqP5HM+dgUAoEhGOUHIP3Ayyp50DfYGVGeUpJK/WN2S/JtglGRwDfYGVEdSGRGl20DYFUCRjNI1JK+3RtmNrsHegBaMkleSFyt7SL4JRskE12BvAOZDv3YZyc93JTDQM2Mlk/8Q0B9RGvJnuENMU3lK48aNG++8806fPn3at2+vdywAVPP3PM7Xr1+/9957ExMThRAdOnSIj49ftmzZa6+99tlnny1dulSZj18I0apVK3tWmpqa+t577ymreuaZZ7SIe/z48cuXL1++fHnlypXVWqfyM7PCjnmc09LSilygZs2aHTp0WLBggVohwdx27dqlvGjZsqWbm1vJC+cPL+zshipKSkoaOnSoUgSK8/TTT1+4cMFlIemFXQEUyUBdw83N7a233lJez5gx4+zZs126dLl48aKnp+fq1atbtGihY2wG2o0uwN6AFgyUVzIXKzvJvAkGygQXYG9AC+SVEclctwVJ9W/sDaAwA/UL6q2BsDegOgMlleTFyh6Sb4KBkkFr7ArAlOjariT5Ka84RnlUxh4yHwI6oyvJnAklM0p/JJ/zsSsAAEUy0AlC8oGTgfakC7A3oDoDJZXkxcoekm+CgZLBBdgbUB1JZVCUbqNgVwBFMlDXkLneGmg3ugB7A1owUF7JXKzsJPMmGCgTXIC9AZgP/dqVZD7flcwoz4zdkuSHgP6IUpI8wx1lmspTGu+88861a9cmT56sdyAA1PT3PM6jRo1SpqsfOnTor7/+Gh4enr9E//79a9Sooby2Z356m832xBNPXL58OSQkZPHixe7u7kUulpOTk5KS4nTcd999d79+/fr16xcYGOj0SgqHpLywWq1FLpD/d4vFUtxKhgwZEhsbe/DgQbWigonZP2LIzc39888/hRBubm6uH0XNnDmzuLnL82VmZk6fPt018eiIXQEUyVhdo1evXs2aNRNCXL16tXHjxseOHRNCfP755126dNE3MGPtRq2xN6AFY+WVtMXKftJugrEyQWvsDWiBvDIoaeu2IKn+jb0BFGasfkG9NQr2BlRnrKSSuVjZSeZNMFYyaIpdAZgSXdvFZD7lFccoj8rYSdpDQGd0MWkzoWRG6Y/kcz52BQCgSMY6Qcg8cDLWntQaewOqM1ZSyVys7CTzJhgrGbTG3oDqSCrjonQbArsCKJKxuoa09dZYu1Fr7A1owVh5JW2xsp+0m2CsTNAaewMwH/q1i0l7viuZUZ4Zs4fMh4D+iNKTOcMdZabK45zz58/Pnj37mWeeiYqK0jsWAGpyF0L89ddfixcvFkJERUV9/PHHnp6eBZdwc3OrWbOmEMLPz69+/fq3XOPEiRO/+eabkJCQjRs3RkZGFl5g//79999/v5+fX2hoaGRk5Ny5c9XZlFLLnxI6f0Lnm+T/PSQkpLiV9O3bNzAwcOHChaqHB/PJ/5mIiIiI+BJt2LAhOztbCFGrVq1y5cq5OM7vvvvOnsXWrl2rdSS6Y1cARTJc15g4caLyIjk5WQgxZcqUJ554QteIhDDgbtQUewNaMFxeyVmsHCLnJhguEzTF3oAWyCvjkrNuC5Lq39gbQGGG6xfUW0Ngb0B1hksqaYuV/aTdBMMlg3bYFYAp0bVdT9pTXnGM8qiM/eQ8BHRG15MzE0pmlP5IPudjVwAAimS4E4S0AyfD7UlNsTegOsMllbTFyn7SboLhkkFT7A2ojqQyNEq3/NgVQJEM1zXkrLeG242aYm9AC4bLKzmLlUPk3ATDZYKm2BuA+dCvXU/O813JjPLMmJ2kPQT0R6hC2gx3lMkqjxPGjRvn7e39xhtv6B0IAJV5CiGmTp2q/M+nn37q4+NTeKHDhw8LIZo1a3bTFM+FzZo1680331QmcS5y5vs9e/bcfffd7u7uL774Ymho6Jo1a55++ukLFy7knzB0FBQUpLwozTzOAQEBffv2/eKLL6ZOnerm5uZcJBs3bkxNTXWubWnYbLZDhw7Vr1/f6ch1l5qaevXq1SInENfamTNnsrKy7F/eZrPFxsYqr4cPH25nq1v+oERB27ZtUwYlpXT8+HF7Fjt58uSKFSvc3d1L/452OnjwYN26dT08PFz2jtLuipycnJMnT9apU8dl71ik9PT0ixcv3nnnnfqGUbKrV69mZmZWrVpV70Ccd+HCBV9f3woVKugdyD9c3DVsNptD9bawBx98sFGjRvv37xdCDBs27KWXXiplSNu2bStlSELiCmOxWI4dO2bPj3moSNq9oeNIo6DLly/n5ubedttt+oZRsnPnzgUEBJQvX17vQP7hyrzKy8sTQpRyJKZ6sdq6dav9nzLOnTsnhLBaraV5RxU3wWKxCCG+//77sLCw0oQkJK4wugylpN0biYmJHh4elSpVctk7FunMmTPlypUr4QqADOLi4qpWrern56d3IP+QM68kueKRm5t74sSJunXrarHyffv2lXIN6p56MjIy0tLSVq1aVcqohKxJJYRISEjw8vIq/bnJIdLujePHj1erVk33cnT48OHatWu78mKRo6xW6+HDh3UvR6WRlZV15syZ2rVr6x3IP1zcL06dOiXVUD8zM/PChQvmrrfx8fHh4eEBAQEue0ch695QhjT16tVz5f4vLC8v78iRI9HR0TrGcEuZmZnnzp2rVauW3oH8w8VJ5ehNq8JUL1Znz551qFhdu3YtIyOjNG+q7ibk5eUdOnTI3PXW9UMpaXdFbm5uXFxcvXr1XPaORUpPT09MTFR+clta58+f9/Pzk+qmlaMOHTpUp04dmT9ElCwjIyMhIUGqPJG2a5fs8OHDUVFRXl5eLn7fnTt3ln4lKp7ysrKycnNzHTrfHT58WLknYicXPCqzb98++zfBBDd0imPQzqjjWVg5gqWh+vXVGzduONQfT5486VAyu6A/7tixQ5WLYHLmsy6fjuXcFbeUlJQkhKhcubLegTjv6NGjkZGRRT5cbQiSPFtYGobIojNnzoSEhOj+9aETJ07cdttt/v7++oZRssOHD9eqVeuWX0mQloT3elx8gvjrr79sNltp1qD6wOn69evmvnCny2PD0u6NY8eOVa9eXffzsuu/xeAoCe/muDipDh06JM/Tj0KIjIyM5ORkh4qVbPd6srKyHL3XUxxpK4wuQyk594bNZjt48GB0dLS+Ax6LxXL8+HHd79eUjKv09pPkk52mn92ysrIyMzNLswbVrzbv3r07/xvTpSFnXunyYLCcu0IIkZ6enpCQEBUV5bJ3LFJKSsr169fvuOMOfcMo2cWLF93c3HQvR6Vx6tSpChUqBAcH6x3IP1zZNa5fvy6EyM3NLc1KVKy3yueOn3/++dSpU6UJSUhcYXR5bFjavXH16tWsrKwqVaq47B2LdOHCBR8fn4oVK+obRslOnjwZFhamylBELa7Mq6tXr4r//zqk01QvVj/++OOxY8fsbHLgwAEhhDyXgpVb4V999VXpby5IW2GSk5Nv3Lhx++23u+wdhcR74+zZs0FBQaGhoS57xyKdOHEiIiLCxd9icIhy00qq68CO0iXz1RUfH1+5cuXAwEC9A/mbtP26ZNevX09OTq5evbouby3VdxZsNtuBAwccuhRvtVrlme4sKyvLYrE4FL8JbugUx6D9UZKzcGkcPHhQ92/e5bt8+XIpR7DqZnhubu6xY8dKmeHKxwqHPixoWnkyMjKuXr3q0EYlJSWp+ACGzWY7d+7c5cuXU1NT09LSsrKyfHx8/P39g4ODK1SocMcdd3h6ev7555/Lly+fMmVKad43MzMzKytLlQLlKAknu3PUoUOHateubdzH1TIzM8+fP6/7LQDVSfUYYVpaWlJSkqMzPlWvXl1YLBZlTqLGjRvbinL+/Hll6RdffLHIBfLNmzfPzc0tJCRkx44dRS5gtVobNWrk5+e3b98+5S8Wi+W+++7z8PA4ePBgyStXUffu3Tt16lT47++//76ypVu3bi2y4cqVK5UFFixYUML6Bw4cWK1aNafDu3r1qre3t3q5AdcJDg62/0Dbf6GzoI8//tiele/evVv1rQMAefTv39/Z06zNZrN98803+Q9Pd+/evTSryv+gCACFxcTESFKsNm/e7NwmfPLJJ5JswjvvvKPOUQEAs7NYLDLUbZvN1rJlS313BQBoJyAgoDQVUt16K/lz2AB05NBNK62LlXPfg61du7Y8myDJU1wAAFM6ffq0JKe8bt26ORG/u7u7/W+h6aMyTn9h2wQ3dKAWq9UqQybYbLZmzZo5Eb+/v7/9b6Fpf3Ru5QAAwECcHebYbGoPnBo1aqTvrgAgLYcuWWhdrJz70feQkBB5NkH54iEAoGSdO3eWpHRfvnxZ310BAJp6+eWXJam3S5cu1XdXAJDZxIkTJSlWn332mXOb8Msvv0iyCUOHDlXnqAAAUEjDhg0lOd/ZbDbnfq2qb9++9r+Fps+M9erVy4mVm+CGDlCCO+64Q54M9/LyUmu7Vq9ebf/7alp5IiIinFh51apVnd2Lttzc3O3bt7/33nsPP/xwgwYNfH19S3gjLy+vmjVrVqhQoVy5chs2bEhPT3f6fe+55x4nthSApurUqeO5e/du5ecH77777iIX2rFjh/Ki5OlXvvjii6effjooKGjjxo3FzWS/b9++/fv3jxgxIv+BOQ8PjylTpjRt2nTKlClLlixxflPUkD/fQXx8fPv27QsvEB8fr7wo4cvG169fX7NmzYsvvuh0GOXLl09ISFAOiutlZ2f7+Pjo8taqUM5zukyEPWbMmJMnT9q//M6dO5UXffr0mT9/fskLN2/e/MSJE+JW3TCf8ozU3Llz7733XvtDKs6DDz5oz2CoRo0aP/30U+nfzn6uT1dpd4WQo/PabLacnBzdwyhZXl6e1WpV8XOF6+Xm5rq7u+d/ypKBi7tGrVq1mjZt6nTzbdu2DRgwIC8vT/nfdevW7dy5084f4SlMqbfz5s0r/acdKkxB0u4Nq9VqsVh0/8mNvLw8m80mye/JFKeMF6u8vLxatWo1btzY6TWoW6yUH7ZauHDhXXfdZWeTuLi4Ll261KhRw7l3FGpvgvLL7Vu2bCn9j5ZLW2F0GUpJuzcsFoubm5vuNSQnJ8fT01Pyubpk+CBwE2nzKicnR/eTuKZhLFq0aNKkSU43V7duCyGaNWuWlJT066+/Or2GfNImlS7FStq9IUk5kiSMkhkiyJLJtgku7hevvPLKwYMHnW6uer2tXbt2s2bNPvnkE6fXkE/mCuPt7e3c00hOk3lvyNABJQmjZLIF6eKkGjNmzKlTp5xurnqxqlmzZkRExMyZM+1v0rt373r16jn9jqpvgr+//9ChQ0eOHOn0GvJRYfJJuyuENDVEkjBKIOF1YEdJcrmgNGTLE5m7dgn02o1r16594YUXSvPW6p7ymjVrtmXLln379tnf5MMPP1y0aJH9y2v6qIxi/PjxTzzxhJ0Lm+CGTnEM2hmFfv1xwYIFpflVUS2uryYnJzt0dF5//fU9e/bYv7ym/dHf318IMWvWLOcmiL+JtPnMENpOhnjCoWSyjbicYPRNMEQWSXJz2RDH2hBBlky2TXDxCWLevHnTpk1zurnqA6emTZtmZmb+8MMPTq8hn7SnWl2uwEi7NyTpgJKEUTLZgnRxUn300Udz5851urnqxapJkyYeHh7ffvut/U1Gjx595swZp99Ri3s9VapUmTFjhtNryEeFKYi9YYgwSiZbkNImVVl4MLh169bNmzd3urm6pVv5EP3ee+/17dvX6ZDySZtXXKArSIZyJMlXrkomSTkqjZycHC8vLxc/TVcyV3aNq1evtmzZsn79+k6vQd16e/vttwshvvnmmwYNGjgdkoIKU5C0e0OS76cbopTp8uhvyVyZV4mJie3bt69Tp47Ta1C3WFWvXl0I8f3339sf0rZt2wYPHpw//Y4T1N0E5bmOo0ePlr4DSlthdBlKSbs3cnNzPTw8uO9mD0MEWQKr1ZqXl6f7ubU0ZDvlSduvS6bjx8kHH3xQnrlrhBCenp4vvPDCU089ZX+TOnXqOLQJmj4z1qxZs59++unAgQP2x2OCGzrFMWh/lOQsXBpSnRwfe+yxSpUqOd1c9QyvUKFCjx49Xn75ZafXIITYu3dv3759HZr1RdPKU69evdq1a99ytQUNHjw4ODjY/uUV6enp33zzzfLlyzdt2pSWlubl5dW4cePGjRs/+uijtWrVqlSpUlBQULly5Tw8PKxW6/Xr17OzsxMSEuLj43/++ecff/zR29u7S5cuXl5e7dq1e/TRRx955JGwsDCHAmjevPn+/fvzd6YrmeB7Q1JVBueYYBMKk2qjnJvxqVKlSp75D3bcdtttRS6UP49zCRX8m2++eeKJJwICAjZs2FDCYhs2bBBCPPDAAwX/2KRJk7CwsK1btzoUuhYaNmyovDh+/HiRC+TP41zCJf7ly5dnZmb+5z//KU0kFSpUUL6ZAwMJCgpy6KP1rl27lBft2rUr+afpr1+/ruSej49P/hzo9ggPDy/N1Hv5Hn30UXumgnr00UdVeTuZsSuAIhmoaxw+fLhHjx6ZmZl16tQZNmzYmDFjhBDjx4/fuHFjaVarSr010G50AfYGtODKvLJYLKVprlGxioiIsH/TMjMzS/NeGm3C7bfffscdd5RmDYIK82/sDWiBvNJLaS4laVG33dzcvLy8uC6hOvYGUJiL+4Wj14EL0qjeBgQEUG9Vx96A6lycVIGBgbIVq8DAQIc2zcfHR7ZNCA0Npd6qi10BmBJd2yGleTZXaHDKc3Nzc3d3d+jQhIaGyvaoTIUKFezfBBPc0CkOndFRJri+GhwcLFt/rFy5MkNodbErAABFcvEJonz58k631Wjg5O3tzahDdewNqM7FSeXoJYuCNCpWPj4+Dm2aCe71FIcKUxB7A6ojqXRUmikMNLraHBYWRulWF7sCKJIru0ZgYGBpmmtUb6tUqcLdPXWxN6AFV+ZVKSck1ahYVa1a1f5NO3nyZGneS6NNiIyMLP0Un1SYgtgbgPnQrx1Vmmm4NTrflS9f3qGj42j8Wj8z5ubmpukzqAVJckOnOPRHCCH8/Pxky/By5cqVMuUuXrzoaBNNK4+bm5u/v79DG+Xocdm+fftHH3307bffpqenN2zY8Pnnn7/rrrvatm0bEBBwy7YWi2XhwoUtW7bcsmXLnj17tmzZ8t133z377LMjR4689957R4wY0bVrV/uD8fDwoGIAsnG/evWq8io5ObnIJZR5nMPCwpQf2ips48aN/fr18/HxWb9+fZs2bUp4s59//lkIUfhHBWvXrn369GknCrS6oqOjfX19hRB79uwpcgHl5z5CQ0OjoqKKW8mCBQs6duxYs2ZNjYKEaeT/ssEtf+MiNjbWZrMJIZo2barLD0mNHDmy5AGQECIoKOiFF15wTTw6YlcARTJK1zh//nyXLl2Sk5MrVaq0fv36kSNHVq1aVQjx448//v777/rGJoyzG12DvQEtGCWvJC9W9pB8E4ySCa7B3oAWyCvDkbxuC5Lq39gbQGFG6RfUW2Nhb0B1Rkkq+YvVLcm/CUZJBhdgVwCmRNd2GflPeUUy0KMytyT5IaAzuozkmVACA/VH8jkfuwIAUCSjnCDkHzgZZU+6BnsDqjNKUslfrG5J/k0wSjK4BnsDqiOpjIjSbSDsCqBIRukaktdbo+xG12BvQAtGySvJi5U9JN8Eo2SCa7A3APOhX7uM5Oe7EhjombGSyX8I6I8oDfkz3CEGrTw2m23dunXKlM1btmwZOXLkgQMH9u/fP2nSpPvuu8+eSZyFEHPmzDly5Mi0adN8fHzatm378ssvb9u27dSpU++8887Zs2e7devWoEGDhQsX5uTkaL05ADTiHhYWprzav39/4X8+f/68Mpl9y5Yti2y/ZcuW3r17e3p6rl+/vn379iW/WWJiohCiSpUqN/09MjJSCBEXF+dg8Crz8fHp0aOHEGLz5s2XL1++6V/zd8VDDz1U3AT2hw4d2rVr15AhQ7QOFUaXnZ2t9DhPT88mTZqUvHD+D0oU1w21VrFixaVLl7q7uxe3gLu7++LFiytVquTKqHTBrgCKZIiukZKS0rVr13Pnzvn5+a1duzYyMtLLyyv/isYbb7yhY2wKQ+xGl2FvQAuGyCv5i9Utyb8JhsgEl2FvQAvklbHIX7cFSfVv7A2gMEP0C+qt4bA3oDpDJJUhilXJDLEJhkgG12BXAKZE13YNQ5zyCjPWozIlk/8Q0BldQ/5MKI6x+iP5nI9dAQAokiFOEIYYOBliT7oMewOqM0RSGaJYlcwQm2CIZHAZ9gZUR1IZDqXbWNgVQJEM0TXkr7eG2I0uw96AFgyRV/IXq1uSfxMMkQkuw94AzId+7Rryn++KY6xnxkpgiENAf4TTDJHh9jNo5dm7d2+7du169OiRnJw8d+7cEydOvPvuu9HR0Q6t5MaNG++8806fPn1umpr1jjvueOmllw4dOrR169bIyMghQ4bUr19/1apVqm4BABdxj4qKUl6tX79+3759Bf8tIyMjJiZGmam9yLq2a9eu7t27CyGUaeNv+WbXr193d3f38PC46e9+fn5CiPT0dGe2QFWDBw8WQmRlZU2ZMuWmf5o0aZIyVX9MTExxzRcsWBAUFPTII49oGiRMYN++fUrPatCggZL/JbD/ByW006NHj7Vr15YvX77wP4WGhn7zzTe9e/d2fVS6YFcARZK8a2RlZfXs2fPgwYPu7u7Lli3LL6f//e9/Q0NDhRCbNm367bffdIxQIfludDH2BrQgeV4ZpViVwCibIHkmuBh7A1ogr4zCKHVbkFT/xt4ACpO8X1BvDYq9AdVJnlQGKlbFMdAmSJ4MrsSuAEyJrq01A53ybmK4R2WKY5RDQGfUmlEyoUiG64/kcz52BQCgSJKfIAw0cJJ8T7oYewOqkzypDFSsimOgTZA8GVyMvQHVkVQGQuk2InYFUCTJu4ZR6q3ku9HF2BvQguR5ZZRiVQKjbILkmeBi7A3AfOjXWjPK+a5IhntmrEgGOgT0RzjBQBluJ8NVnitXrjz55JMtWrS4cuXKN99889dff/33v//18fFxYlXvvPPOtWvXJk+eXNwC7du3/+677/7444/y5cs/+uij3bp1O3HiRCliB6AD90aNGjVs2FAIYbPZunbtun79+uzs7GvXrn399detWrX6+eefleUKz+McHx/fpUuXGzdudO3a9fDhwx9//PFHH3304YcfTivk7NmzSpPU1FRPT8/CQSh/TEtLsz/uRx99tFq1atWqVTt9+rTjW12s7t27d+3aVQgxffr0zz77LP/vH3/88eeffy6E6NWrV4cOHYpsm5ubu3Tp0v79+/v7+6sYEkwp/5cf7BkxOLSwdrp16xYfH//uu+8qYQQGBrZq1WrSpEnx8fE9evTQMTDXy98VrVu3DgkJEUI0aNCgbO4KoKCCXcPNzc3f31+SKmG1Wh977LGtW7cKIaZPn17wQkZgYOCzzz6rvJbkF4cK7kblI3S9evVk2I26KLg3AgMDhRCSJBUMjWKlHWNtQsFMCAoKEkI0b95chkzQRcG94evr6+npKUm/gKHl55Xy04jBwcHklWyMVbfFv4uVj49PGS9WBfeGu7u7n59fWd4bgKJgv/Dz83N3d5ekXxi63np6evr6+kqyJ3WRvzeaN28uyvZVcajlpmLl4eEhSVIZrlgVZrhNKJgMQoiAgABJksH1Cu6KcuXKCSGio6PL5q4AzKRg1/by8vLx8SmzVU51hjvlFWTER2UKM9YhKHyerV+/Pp1RFcbKhMKM2B/z87lRo0aibN93KPwoRYsWLcrmrgAAFFT4SRhJThCGGzjddGPay8urzI46BDemoYHCo9mWLVvKkFSGK1aFGW4TCiaDh4cHN6aVvdGsWTMhRFBQUFneG1DFTQ8Gy3NjGgUZt3QrDwaX5WJV+PNX06ZNy+auAArK7xrKfBTyPGtnrHpb+NvrjRo1kmE36qLg3vD395fnwWAYWn5etWjRQlCsVGWsTShYYQICAtzc3CTJBF0U3Bve3t5l/Ko4YA48m60dY53vCjPiM2M3Mdwh4DwLhxguw+1hrMrz66+/NmzY8IsvvnjjjTf++uuvXr16ubm5Obeq8+fPz549+5lnnomKiip5yTZt2uzYsWPx4sV79+5t2LDhhx9+6Nw7AtCHzWZbs2aNu7t7/l+8vLyU2tG6dev69esrf7xy5Yrt39atW2fnW/z8889Kk4oVK7q7u9sKefLJJ4UQ69atK/xPxenUqZOy8hMnTtjfStG9e/dOnToV96/nz5+PiIhQVt60adNHHnkkvw5Wr149MTGxuIZr1qwRQmzfvt3ReGAOgwcPbty4sZ0LDxw4UEmqBQsWlLxk/jToFStWtD+YuLg4IcS3335rfxP7ZWdnCyFmz56txcoNR5nsft++fXoHAsilfPnyr7/+ukYr9/DweP/99+1ffvjw4UohHTFiROF/vXTpUv7P9WzYsMHRYI4fPy6EWLt2raMN7REbGyuE2Lx5sxYrN5zp06cLIaxWq96BwFQCAwPfeustLdacm5srhPjwww/tb6JpsTp48KCjDZ1ooukmrF69Wghx+vRpRxvaY/78+UKI5ORkLVZuODExMQ0aNNA7CphKfHy8EOLrr7/WOxDzmzlzphDCYrHYubymddtmsz3zzDM1a9Z0oqE9Bg4c2KxZM41WbjjVqlV74YUX9I4CkMvo0aOrVKmi0cqHDh1av359+5fXut62b9/+4YcfdqKhPaKjo4cMGaLRyo0lOTlZCDF//ny9A4GpPPfcczVq1NBo5YMGDWrSpIn9y2tdrFq0aDFgwABNm2i9CUFBQW+++aYTDW8pLy9PCDFjxgwtVm44mzZtEkLs3r1b70AAqKlNmzZ9+/bVOwpJLVu2TAhRwpNIhWl6ypswYUJISIh2TbR+VMaJuzMmuKFjv99//10IsWPHDi1WbgKO3o/Wevz51FNP1a5dW7smWvfHc+fOCSFWrFhhfxP7adpTDGfOnDlCiPT0dL0DAQDI5dNPPxVCpKWlabHyKVOmeHp62r+81gOnIUOGREdHO9HQHn369GnXrp1GKzecsLCwV155Re8oYCrKF1Bzc3O1WPnEiRMDAgLsX17rYuXEgy6PP/5406ZN7V9e601o3rz5Y4895kRDe0RFRQ0fPlyjlRtLYmKiEGLZsmV6BwJTGTZsWL169fSOokwIDw9/6aWX7F9e09Kt6YMup0+fFkKsXr1ai5UbztKlS4UQSUlJegcCSCQrK0sI8dFHH2mx8qSkJCHE0qVL7W+iab3dvHmzECI2NtbRhvZYu3atEOL48eNarNxwXnrppfDwcL2jgKmkpqYKIebNm6fFypV7rCtXrrS/iabF6qeffhJC7N+/X9Mmmm7C7NmzhRDZ2dmONrTH22+/7efnp8WajahLly7333+/3lEAUNOvv/4qhNi7d6/egUiqQYMGMTEx9i+v9aV4Ly+v9957z6Em3t7ekydPtnNhrZ8Zc/TujBNNJLyhY7/u3bt37txZo5VDTp06derZs6f9y2ud4REREWPHjnWiYUHbtm0TjkyzqXXluffeex988EH7ly+uSW5u7ssvv+zu7t62bVtVprV57LHHypUrV3ji1hJcu3atT58+QohHH3208Ow348aNq1y5cukDA6AudyFE7969Fy5c6O/vr1Qxi8XSpEmTBQsWbNu27cqVK0KImjVrVqhQQZRauXLlrFar8h2YgpRpYZWfcNFdlSpV9u7d27lzZyHE3r17V69erUyJ+8ADD+zcuTM8PLy4hgsWLKhTp07r1q1dFysMK/+XH5RfFlVlSQBAYZMmTVK+tNazZ09lYrubhIWFxcTEKK+N9YtDAMzEBMXKBJsAAGUKdRsAXIN6C8AQTFCsTLAJAADYw+inPBM8KmP0QwC1mCATTNAfAQCAIZhg4ASgLDBBsTLBJgBAWUPpBgDXoN4CMAQTFCsTbAIAALdkgvOd0Z8ZM8EhAEpg1gw3ROVJSUm5995733///XHjxm3evPmOO+4o5Qr//PPP5cuXv/baaw5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9MjIylN9PqFWrlp1NHJIf54kTJxxt2717906dOhX++wcffKCs86+//iqy4fbt25UFpk+fXuQCr776qq+vb3JysqMhwQQGDx7cuHFjR1vlj+qOHTtW8pJffPGFsmSPHj1uudq4uDghxLfffutoPPZQJnOfPXu2Fiu/pRUrVgQEBBQuZX5+fkuWLCk7MQASclnX8PDweP/9951ru3LlyvzhTUpKivLHPXv2BAYGCiHCwsKOHz/u0AqPHz8uhFi7dq1z8ZQsNjZWCLF582YtVl4ySQqdJGHAZFyTV7m5uUKIDz/80LnmqhergwcPCiE2bNjgXDymN3/+fCGELp/jJCl0koQBkyGvoKmBAwc2a9ZMl7eWJLclCQOQisv6xdChQ+vXr+9cW9WH+jabrX379g8//LBz8dxSdHT0kCFDNFp5ySQpdJKEATNxWVINGjSoSZMmzrXVoli1aNFiwIABzsVjenl5eUKIGTNm6PLuMhQ6GWIAoDqXde26des++eSTjrbS6DmNZcuWCSESExPtj8SJJgWpftaeMGFCSEiIc8FATi7rjN9//70Q4siRI841Vz2Zp02bJv79VOQt/fTTT0KI/fv3O9TKpllJadu27SOPPOJoMGWEjrc+JRm7ShIGAEA2LjtBTJkyxdPT07m2Wlx7HDJkSHR0tHPx3FKfPn3atWun0cpLJskZX5IwYCYuS6qJEycGBAQ411aLYqXjgy6GEBUVNXz4cF3eWpJCJ0kYMBOSCpo6ffq0EGL16tWuf2tJcluSMADZuKZrJCUlCSGWLl3qXHPVR/ubN28WQsTGxjoXT8nWrl0rhHDiA0jpSVLoJAkDJuOavDp79qwQYuXKlc41V71YOX03vIx4++23/fz8dHlrSQqdJGEAUJHL+vXXX38thIiPj3e0oUYPXDVo0CAmJsahSJxokk+LuwleXl7vvfeec/FATi7rjx06dOjdu7dzbbVI5rCwsFdeeUXrJjbN6smsWbOEEDk5OfZH4kQTtaxYsUIIsWbNGifabtu2TQixfft21aMqa5Qpxbdu3Wqz2VJSUoQQn3/+ud5BAXAF9/yze3x8fIsWLTZt2iSE8Pf3f+yxx95+++1hw4alpaX17t1bmaawZcuWhYcFRZozZ05OTo4QYsSIEXY20Z1S/oQQygzUhXl5eSkvbty4UeQCMTExWVlZy5cv1yA6mNClS5eU+9ahoaFRUVElL5z/6x/2d0PzWblyZf/+/dPT0wv/U2Zm5uDBg5csWVIWYgAkZJSu8cgjjzRq1EgIcf369Y8++kgIcfr06W7duqWlpQUEBHz//fe3rMZlgSRHU5IwYDJGySuKVRkhSUJKEgZMhryCWUmS25KEAUjFKP2Cob6dJDmgkoQBMzFKUlGsyg4ZclKGGACoTvKubabnNDhro2SSd8aCjJvMZiopuCVJ+pQkYQAAZGOUE4RxB34uJskBlSQMmIlRkopiVXZIkpOShAEzIalgVpLktiRhALIxStdgtG8PSY6mJGHAZIySVxSrMkKShJQkDAAqkr9fm+aBK07ZuCX5+6PCuMlsmnpSGjk5Oa+99lqbNm0eeughvWMBgLLo73mcr1+/fu+99yYmJgohOnToEB8fv2zZstdee+2zzz5bunSp8jsJQohWrVrZs9LU1NT33ntPWdUzzzxT3GJ5eXlpaWnOxT1+/Pjly5cvX768cuXKzq2hsOTkZOXFLedxLi7smjVrdujQYcGCBWqFBHPbtWuX8qJly5Zubm4lL5w/FrSzG5pPUlLS0KFDlVpUnKeffvrChQvmjgGQkIG6hpub21tvvaW8njFjxtmzZ7t06XLx4kVPT8/Vq1e3aNFC3/BkIMnRlCQMmIyB8opiVRZIkpCShAGTIa9gVpLktiRhAFIxUL9gqG8PSQ6oJGHATAyUVBSrMkKGnJQhBgCqk79rm+k5Dc7aKIH8nbEg4yazmUoKSiZJn5IkDACAbAx0gjDuwM+VJDmgkoQBMzFQUlGsyghJclKSMGAmJBXMSpLcliQMQDYG6hqM9m9JkqMpSRgwGQPlFcWqLJAkISUJA4CKDNGvTfPAFadslMwQ/VFh3GQ2TT0pjdmzZ8fHx0+dOvWWewAAoIW/53EeNWqU8tsCQ4cO/fXXX8PDw/OX6N+/f40aNZTX9vyYgM1me+KJJy5fvhwSErJ48WJ3d/ciFzt9+vTdd989f/585+K+++67+/Xr169fv8DAQOfWUFhOTo7ywmq1FrlA/t8tFktxKxkyZEhsbOzBgwfVigomZv/wLjc3988//xRCuLm5yTy61dTMmTNvOfN7Zmbm9OnTzR0DICFjdY1evXo1a9ZMCHH16tXGjRsfO3ZMCPH555936dJF79CkIMnRlCQMmIyx8opiZXqSJKQkYcBkyCuYlSS5LUkYgFSM1S8Y6t+SJAdUkjBgJsZKKopVWSBDTsoQAwDVyd+1TfacBmdtFEf+zngTgyazyUoKSiBJn5IkDACAbIx1gjDowM+VJDmgkoQBMzFWUlGsygJJclKSMGAmJBXMSpLcliQMQDbG6hqM9ksmydGUJAyYjLHyimJlepIkpCRhAFCRIfq1mR644pSNEhiiP+YzaDKbqZ44Jzk5efLkyf3792/btq3esQBAGeUuhPjrr78WL14shIiKivr44489PT0LLuHm5lazZk0hhJ+fX/369W+5xokTJ37zzTchISEbN26MjIy86V9XrFgxYsSIzp0733nnnVu3blVtO9SQPyV0/oTON8n/e0hISHEr6du3b2Bg4MKFC1UPD+aT/5seERER8SXasGFDdna2EKJWrVrlypXTM2j9fPfdd/YstnbtWnPHAEjIcF1j4sSJyovk5GQhxJQpU5544gldI5KIJEdTkjBgMobLK4qVuUmSkJKEAZMhr2BWkuS2JGEAUjFcv2CoXzJJDqgkYcBMDJdUFCvTkyEnZYgBgOrk79rme06DszaKJH9nLMyIyWy+koLiSNKnJAkDACAbw50gjDjwcyVJDqgkYcBMDJdUFCvTkyQnJQkDZkJSwawkyW1JwgBkY7iuwWi/BJIcTUnCgMkYLq8oVuYmSUJKEgYAFRmiX5vsgStO2SiOIfpjQUZMZpPVEydMnDjxxo0bkyZN0jsQACi7PIUQU6dOVf7n008/9fHxKbzQ4cOHhRDNmjW7aYrnwmbNmvXmm28qkzgX+TMFc+bMOXHiRHR0dNu2bX///ffShq+qoKAg5UVp5nEOCAjo27fvF198MXXqVDc3NyfCyMjIGDRoUGpqqhNtSyk3N/fo0aN16tTx8vJy/bur4urVq8nJycrM4y526NAhh5a32WyxsbHK6+HDh9vZ6pa//qHIysoSQowfP3727NkORWUPq9UqhJg6deq3336r+spLcOTIEXsWi4+Pv/fee53rfYaIoUhpaWlnzpypV6+eK9+0sOTk5EuXLtWuXVvHGG4pKSkpMzOzevXqegfivDNnzvj4+ISHh+sdyD9c3DWsVuvZs2dLs4YHH3ywUaNG+/fvF0IMGzbspZdecnpVmZmZQog33nhj1qxZpQmpSNeuXRNCjBw5MiwsTPWVF0eSQidJGIVduXIlJSVFl5FGQQkJCRaL5fbbb9c3jJKdOnXK39+/cuXKegfyD1fmlc1mE0LIU6zS09OFEK+88kr+Rz+XycnJOXbsWN26dW/5WVJHp06dEkI89NBDrvwcJEmhkySMws6dO+fu7l6lShWXvWOR4uPjg4ODXXkidsKRI0duu+22Ei5TuJ6ceSVJOUpPTz916lT9+vX1/exWsmvXrl25cqVWrVp6B1KS3bt3Z2Zm3nfffa58U0lyW5IwCjty5EiVKlWCg4Nd9o6FWa3WQ4cO1axZ08/PT8cwSpadnX38+HHdy1Fp3Lhx49y5c/Xq1dM7kH+4uF8cPnzYYrGUZg0qDvWFEAkJCcePH9eoJB4/fvzChQul/GjjKEkKnSRh3MRisRw5cqRWrVpF3stzmaysrLi4uPr167u7u+sYRslSU1MvXLhQt25dvQP5h4uT6tChQ6VcibrF6uLFi+fOnXPx+E0h/yc75TrSjBkzvv/+e1e+rwyFToYYiiTJZ7eUlJSkpCTJ77udPn3a19dXqptWDrFarYcPH77zzjtl/hBRsuvXrycmJtapU0fvQP7h4q599uzZ06dP27+8ps9pJCYmCiH69evn7e1t55ovXrwohMjNzbVz+SKpeNY+ffp0enq6Lqfss2fPenp63nbbba5/a1XYbLZDhw7VqFHD399f71j+5uLOeOXKFfH/d8+dpmIyK59kHUpm5e68ck/NTpqWlISEhBMnTujSH0+ePBkUFCTzEFp5rnLMmDGuvPUpydhVkjAcdf78eSFE1apV9Q7ESTab7fDhw3fccUdgYKDesThJkmcLS8MQWSRJ/Tx69GhERIRUt49vYoIPYhLe63HxCeLMmTPKk+ROU/fa46lTp06fPq3RwGnXrl25ubncmNYxjMIOHz5crVq1/C/+6CIvL+/w4cNRUVG+vr46hlEy5W5OvXr1PDw89I7lby5OqlOnThX3vTA7qVusTp8+HRcXp8unPEMMpU6fPr1y5cq4uDhXvqkkhU6SMG4iybcLMzIyTp48Wa9ePZlvTHOV3n6SlKOTJ08GBgZWqlRJ3zBKJv8nu4yMDCHE66+//umnn7rsTSXJbUnCKCwlJeXixYu6l6NLly6lpaXVqFFD3zBKJsn3FErjxIkToaGhFSpU0DuQf7iyayjj/ISEhNKsRMXRvjK51bPPPqvFE9QXLlwQQgwePNiVV6clKXSShFFYYmJiTk7OHXfc4bJ3LNKZM2e8vb0jIiL0DaNkx48fr1ixYvny5fUO5B+uzCtloo+kpKTSrETFYqXcDX/qqadcf7fLEJ/sjhw5kpWVxXVgHcMoTJLPbseOHatUqVJoaKi+YZRAuWkl1XVgRxniQ0TJjh8/HhYWJk+euLhfX758Wfz/ic9Omj5wdenSpY0bNzpU0k+dOlWxYkX7ly9M3bsJeXl5n3/++c8//1yalThB+f617teES0OSeWAKcnF/PHDgQCnLqbrJnJaW9uWXX+b3d3tcv35dnmfCz507J4To2rWr/YdGaVJ6mZmZcf/v7Nmz6enpaWlpqampHh4ewcHBAQEBwcHBNWrUqFmzpre395w5c55//vk777zT6be7fv26EGLkyJGuvyItySVNtSjPtY4aNerChQuRkZFCiOnTpy9fvlzvuNRhiAsRJTDB42rXr19PSEiQ6quypaccF3m+f5GcnHz58mVHp1ipV6+eZ15envKzDI0bN+7cuXPhhS5cuKDcKG3ZsmXJq/vss8+ef/75EiZxFkL89ttvysnplVdekXYe5xs3bhS5gPKdK1HiPM5CiJycHC8vL6eHR+7u7sHBwbp8Ts7NzfX39y9Xrpz9XyqTTW5ubm5uri4fcb29vR2avyMuLk65Q+MQO8eCSvoFBgZqsSuUp2/9/PxcvJ/t71OhoaEaXQeUIYYieXp6Xr582cVvWpjVas3IyJDnGlORMjIyPDw8JA+yZFevXvX19ZVqE1zfNUp5lvz2228PHjyovFa+He005daRRvVWOa0EBQW58nBLUugkCaOw3Nxci8WiewdMS0vTa8BjvytXrgQEBEgVpCvzSpl/p5Tf1zJKsSpZdna28hFD5gv3yu518ecgSQqdJGEUlpKS4u7urnsNCQoKCg4O1j2MkgUEBJQrV06q336UM6+UchQaGqrvl2m9vLyU86PM35PPy8vLzMyUPPM9PT1d/8lOktyWJIzCAgICQkJC9C1HVqtVqYqSXLIvkiTlqDTc3d2vXr0qVZVwcb/w8fEp5fQEKg71hRDu7u5eXl4aHRF3d3dvb2/qrY5h3MRisSg1RN95nDMzM5UPejI/8enm5paSklKWi5W3t3deXl5p1qB6sXJ9PVEEBgZK/slOuY7EfTe9YiiSl5eXUm/1/exms9nS0tJkzl4hxNWrV12fvSqyWq1K/MZ9HksIkZqaKtUhcHHX9vDwcOiLXpo+p6GMjkJCQuyfxUl5PKmU+0HFs7aHh4ebm5suGZWcnOzp6SlVMjvEZrP5+/uHhITIM8Wnizuj8m0cqZJZCOFQRilf+3doEzQtKQyhb8nFtz4lGbtKEoajUlNTbTab/ElVAuVKiL7zRZaG8myhVHMlOMoQWSRJ/VTu1+geRgmsVqvSp2S+m1MyCe/1uPgEcenSpVKuQd1rjx4eHtrdO/b09LRarWXwwp08YRSm1BB9f2A4Ly9PuTEt8zWlzMxM5QEVee7muDip8r/85TQDFauSGWIo5ebmxo1pfcO4iSTfLvT29lbGXTLP9iXK/FV6+12/fl2v688FSfLZrWTK1WaZg1S+F+Dib4tIktuShFGYJDeXlZsFuodRMknKUWlIWMpc2TWys7OFTF/XUj5zaXRElKmUgoODXTmVkiSFTpIwCktPT8/Ozta9A167dk2vO4n2K+PFSvndi1J+llH9u6UuricK5ZNd+fLl5bl3WZjynA/XJXQMo7CgoCAXz65QJOU6sO5hlCArK0u5hiPPTStHZWVlGX18rsynKc8muLhfO3HKk+2BK0efQS1M3bsJQo+vFQghcnJylIuxMk8HUbKcnBwZ5oEpyMX9UfnOdWnWoG4yu7m5OTo1lpubm0Ob4IJnwsuVK2d/ibh69aqjweRLT0/ftGnT5s2bt2zZsmfPHmWyKW9v79tuuy00NDQwMNDX1zcvL+/8+fPZ2dmXLl1KSEhQvt/q5ua2a9euSZMmderUqV27dk4UNKWJLkMvSS5pqkX5alhQUJAyPBNCKHVV57BUcu3aNR8fH+NujgkeVxNCXL9+3biHoEj5xyUgIEDvWIQQIi8vz4nJM4OCgsSOHTuU/3nhhRdsRVm9erWywPLly4tcQLFs2TJlAuIdO3aUsFi+l19+WQgxc+ZMexZWV/fu3Tt16lT47wsWLFC2dNGiRUU2nDx5srLAmjVrilt5SkqKn5/fa6+9plq4MIjBgwc3btzY/uWXLFmipFOfPn1SbiX/915iY2PtWbnyQ/Tffvuts1tTEuVG1+zZs7VYeQkaNGhgT12rXbu2uWMAJOTiruHh4fH+++873fz333+/6clpO4cuRTp+/LgQYu3atU6voQTKTz9t3rxZi5UXR5JCJ0kYMBlX5lVubq4Q4sMPP3R6DeoWK+Wa6YYNG5xeg7nNnz9fCJGcnOzKN5Wk0EkSBkyGvIILDBw4sFmzZi5+U0lyW5IwAKm4uF8MHTq0fv36TjdXd6hvs9nat2//8MMPl2YNJYiOjh4yZIhGKy+OJIVOkjBgJi5OqkGDBjVp0sTp5qoXqxYtWgwYMKA0azAxZcbtGTNmuPh9ZSh0MsQAQHUu7tp169Z98skn7V9e0+c0li1bJoRITEy0Px4nmtxE3bP2hAkTQkJCnG4Oqbi4M37//fdCiCNHjji9BnWTedq0aUIIh5r89NNPQoj9+/fb30TTktK2bdtHHnnEoU0oO3S59SnJ2FWSMAAAsnHxCWLKlCmenp5ON1f92uOQIUOio6NLs4YS9OnTp127dhqtvDiSnPElCQNm4uKkmjhxYkBAgNPNVS9WujzoYiBRUVHDhw938ZtKUugkCQNmQlLBBU6fPi2EWL16tSvfVJLcliQMQDau7BpJSUlCiKVLlzq9BnVH+5s3bxZ23/1x1Nq1a4UQx48f12LlxZGk0EkSBkzGlXl19uxZIcTKlSudXoO6xcqJu+Flyttvv+3n5+fiN5Wk0EkSBgAVubhff/3110KI+Ph4+5to+sBVgwYNYmJiHNoEJ5oUpPrdBC8vr/fee680a4A8XNwfO3To0Lt3b6ebq57MYWFhr7zyiqZNNK0ns2bNEkLk5OTYH48TTXJyctatWzdw4EBlDtNy5cp17979/fff37BhQ3x8vMViKa5hVlbWl19+6ebmdv/993fo0EH5YZKIiIiRI0f+8ccfVqvV/hi2bdsmhNi+fbv9TVCknTt3CiG2bt1qs9lSUlKEEJ9//rneQQFwBfczZ84o55jbbrutyJN9/kTPJfyYwDfffPPEE08EBARs2LDBzt8ckFDDhg2VF8qcjIXFx8crL+rXr1/cSpYvX56Zmfmf//xH7ehgNrt27VJetGvXLqRE4v9zz8fHp1GjRnoGrauHHnrInsV69+5t7hgACRmoaxw+fLhHjx6ZmZl16tSZOnWq8sfx48frG5VUJDmakoQBkzFQXlGsygJJElKSMGAy5BXMSpLcliQMQCoG6hcM9e0hyQGVJAyYiYGSimJVRsiQkzLEAEB1kndtkz2nwVkbJZC8M97EoMlsspKCkknSpyQJAwAgGwOdIAw68HMxSQ6oJGHATAyUVBSrMkKSnJQkDJgJSQWzkiS3JQkDkI2Bugaj/VuS5GhKEgZMxkB5RbEqCyRJSEnCAKAi+fu1mR644pSNksnfH/MZNJkNXU+Sk5PffffdatWqde/e/ffffx8xYsTu3buvXLny3XffjR079oEHHqhRo4aHh0dxzX18fD766KPIyMjvvvtuy5YtKSkpGzdu7NKly5IlS9q2bduoUaPFixfn5OS4cosAoMxyv3r1qvIqOTm5yCWUeZzDwsKqV69e5AIbN27s16+fj4/P+vXr27Rpo02crhAdHa38tsCePXuKXODAgQNCiNDQ0KioqOJWsmDBgo4dO+b/AgNQHOUnFESJM6QrlN/xEEI0bdrUy8tL88hkNXLkSGVkXIKgoKAXXnjB3DEAEjJK1zh//nyXLl2Sk5MrVaq0fv36kSNHVq1aVQjx448//v777/rGJg9JjqYkYcBkjJJXFKsyQpKElCQMmAx5BbOSJLclCQOQilH6BUN9O0lyQCUJA2ZilKSiWJUdMuSkDDEAUJ3kXdtMz2lw1kbJJO+MBRk3mc1UUnBLkvQpScIAAMjGKCcI4w78XEySAypJGDAToyQVxarskCQnJQkDZkJSwawkyW1JwgBkY5SuwWjfHpIcTUnCgMkYJa8oVmWEJAkpSRgAVCR/vzbNA1ecsnFL8vdHhXGT2aD15MqVK6NHj77jjjsmTJhwzz33bN269dSpU5MnT27WrFkJEzffZOXKldu2bZs6daq3t7cQwsfH5/7771+wYMHFixfXrFkTGhr6n//8p0aNGjNnzszNzdVyawAAwj0sLEx5tX///sL/fP78eeWXB1q2bFlk+y1btvTu3dvT03P9+vXt27fXLlAX8PHx6dGjhxBi8+bNly9fvulf83fFQw895ObmVuQaDh06tGvXriFDhmgdKowuOztb6XGenp5NmjQpeeH8X/8orhuWERUrVly6dKm7u3txC7i7uy9evLhSpUrmjgGQkCG6RkpKSteuXc+dO+fn57d27drIyEgvL6/8KxpvvPGGjrFJRZKjKUkYMBlD5BXFquyQJCElCQMmQ17BrCTJbUnCAKRiiH7BUN9+khxQScKAmRgiqShWZYoMOSlDDABUJ3PXNtNzGpy1cUsyd8aCjJvMZiopsIckfUqSMAAAsjHECcK4Az/Xk+SAShIGzMQQSUWxKlMkyUlJwoCZkFQwK0lyW5IwANkYomsw2reTJEdTkjBgMobIK4pV2SFJQkoSBgAVSd6vTfPAFads2EPy/qgwbjIbsZ7k5eV98skntWrV+vTTT5944om4uLhly5a1b9++uKksi5OTk/Paa6+1adPmoYceuumffHx8evfuvXnz5h07drRu3frFF19s0KDBhg0bVNsGAEAh7lFRUcqr9evX79u3r+C/ZWRkxMTE5OTkiGJOQrt27erevbsQYt26dXfddZfmwWpv8ODBQoisrKwpU6bc9E+TJk1SflchJiamuOYLFiwICgp65JFHNA0SJrBv3z6lZzVo0MDPz6/khe3/9Q/T69Gjx9q1a8uXL1/4n0JDQ7/55pvevXuXhRgACUneNbKysnr27Hnw4EF3d/dly5bll9P//ve/oaGhQohNmzb99ttvOkYoFUmOpiRhwGQkzyuKVVkjSUJKEgZMhryCWUmS25KEAUhF8n7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      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=7661x515 at 0x1CAB1ABFFD0>"
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     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit_drawer(grover)"
   ]
  },
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   "source": [
    "## References\n",
    "\n",
    "[1] \"[A fast quantum mechanical algorithm for database search](https://arxiv.org/abs/quant-ph/9605043)\", L. K. Grover, Proceedings of the 28th Annual ACM Symposium on the Theory of Computing (STOC 1996)\n",
    "\n",
    "[2] \"[Tight bounds on quantum searching](https://arxiv.org/abs/quant-ph/9605034)\", Boyer et al., Fortsch.Phys.46:493-506,1998"
   ]
  }
 ],
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